966 resultados para Complete K-ary Tree


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First appeared in the Cornhill magazine.

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Maps by Keith Johnston; engraved and printed by W. & A. K. Johnston, Edinburgh.

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"One thousand copies have been printed on large paper." This is copy no. 947.

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Ms. notes in margins throughout volume and on 3 blank pages at end.

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Let K(r, s, t) denote the complete tripartite graph with partite sets of size r, s and t, where r less than or equal to s less than or equal to t. Let D be the graph consisting of a triangle with an edge attached. We show that K(r, s, t) may be decomposed into copies of D if and only if 4 divides rs + st + rt and t less than or equal to 3rs/(r + s).

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A graph G is a common multiple of two graphs H-1 and H-2 if there exists a decomposition of G into edge-disjoint copies of H-1 and also a decomposition of G into edge-disjoint copies of H-2. In this paper, we consider the case where H-1 is the 4-cycle C-4 and H-2 is the complete graph with n vertices K-n. We determine, for all positive integers n, the set of integers q for which there exists a common multiple of C-4 and K-n having precisely q edges. (C) 2003 Elsevier B.V. All rights reserved.

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A cube factorization of the complete graph on n vertices, K-n, is a 3-factorization of & in which the components of each factor are cubes. We show that there exists a cube factorization of & if and only if n equivalent to 16 (mod 24), thus providing a new family of uniform 3 -factorizations as well as a partial solution to an open problem posed by Kotzig in 1979. (C) 2004 Wiley Periodicals, Inc.

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A K-t,K-t-design of order n is an edge-disjoint decomposition of K-n into copies of K-t,K-t. When t is odd, an extended metamorphosis of a K-t,K-t-design of order n into a 2t-cycle system of order n is obtained by taking (t - 1)/2 edge-disjoint cycles of length 2t from each K-t,K-t block, and rearranging all the remaining 1-factors in each K-t,K-t block into further 2t-cycles. The 'extended' refers to the fact that as many subgraphs isomorphic to a 2t-cycle as possible are removed from each K-t,K-t block, rather than merely one subgraph. In this paper an extended metamorphosis of a K-t,K-t-design of order congruent to 1 (mod 4t(2)) into a 2t-cycle system of the same order is given for all odd t > 3. A metamorphosis of a 2-fold K-t,K-t-design of any order congruent to 1 (mod 4t(2)) into a 2t-cycle system of the same order is also given, for all odd t > 3. (The case t = 3 appeared in Ars Combin. 64 (2002) 65-80.) When t is even, the graph K-t,K-t is easily seen to contain t/2 edge-disjoint cycles of length 2t, and so the metamorphosis in that case is straightforward. (C) 2004 Elsevier B.V. All rights reserved.

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Cytochromes from the SoxAX family have a major role in thiosulfate oxidation via the thiosulfate-oxidizing multi-enzyme system (TOMES). Previously characterized SoxAX proteins from Rhodovulum sulficlophilum and Paracoccus pantotrophus contain three heme c groups, two of which are located on the SoxA subunit. In contrast, the SoxAX protein purified from Starkeya novella was found to contain only two heme groups. Mass spectrometry showed that a disulfide bond replaced the second heme group found in the diheme SoxA subunits. Apparent molecular masses of 27,229 +/- 10.3 Da and 20,258.6 +/- 1 Da were determined for SoxA and SoxX with an overall mass of 49.7 kDa, indicating a heterodimeric structure. Optical redox potentiometry found that the two heme cofactors are reduced at similar potentials (versus NHE) that are as follows: + 133 mV (pH 6.0); + 104 mV (pH 7.0); +49 (pH 7.9) and +10 mV (pH 8.7). EPR spectroscopy revealed that both ferric heme groups are in the low spin state, and the spectra were consistent with one heme having a His/Cys axial ligation and the other having a His/Met axial ligation. The His/Cys ligated heme is present in different conformational states and gives rise to three distinct signals. Amino acid sequencing was used to unambiguously assign the protein to the encoding genes, soxAX, which are part of a complete sox gene cluster found in S. novella. Phylogenetic analysis of soxA- and soxX-related gene sequences indicates a parallel development of SoxA and SoxY, with the diheme and monoheme SoxA sequences located on clearly separated branches of a phylogenetic tree.